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Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element…
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency…
A Green's function approach to the inclusive quasielastic ($e,e'$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the…
We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
The quantum behavior of charge carriers in semiconductor structures is often described in terms of the effective mass Schr\"{o}dinger equation, neglecting the rapid fluctuations of the wave function on the scale of the atomic lattice. For…
We present an overview of electronic device modeling using non-equilibrium Green function techniques. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. The rise in popularity was…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the…
Multicentric integrals that involve a continuum state cannot be evaluated with the usual quantum chemistry tools and require a special treatment. We consider an initial molecular bound state described by multicenter spherical or cartesian…
In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's…
We show how two-point correlation functions derived within non-isotropic random wave models are in fact quantum results that are obtained in the appropriate limit in terms of the exact Green function of the quantum system. Since no…
We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…
One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However,…